McALLEN, Texas >> For nearly two months, images of immigrant children who have crossed the border without a parent, only to wind up in concrete holding cells once in United States, have tugged at heartstrings. Yet most Americans now say U.S. law should be changed so they can be sent home quickly, without a deportation hearing.

A new Associated Press-GfK poll finds two-thirds of Americans now say illegal immigration is a serious problem for the country, up 14 points since May and on par with concern about the issue in May 2010, when Arizona’s passage of a strict anti-immigration measure brought the issue to national prominence.

Nearly two-thirds, 62 percent, say immigration is an important issue for them personally, a figure that’s up 10 points since March. President Barack Obama’s approval rating for his handling of immigration dropped in the poll, with just 31 percent approving of his performance on the issue, down from 38 percent in May.

More than 57,000 unaccompanied immigrant children have illegally entered the country since October. Most of the children hail from Honduras, Guatemala and El Salvador, where gang violence is pervasive. Many are seeking to reunite with a parent already living in the United States.

Since initially calling the surge an “urgent humanitarian situation” in early June, Obama has pressed Central American leaders to stem the flow and has asked Congress for $3.7 billion in new money to hire more immigration judges, build more detention space and process children faster.

House Republicans on Tuesday put forward a bill costing $659 million through the final two months of the fiscal year that would send National Guard troops to the U.S.-Mexico border and allow authorities to deport children more quickly.

By a 2-to-1 margin, Americans oppose the current process for handling unaccompanied minors crossing the border, which requires that those who are not from Mexico or Canada stay in the U.S. and receive a hearing before a judge before they can be deported. Changing the law to allow all children crossing illegally to be sent back without such a hearing drew support from 51 percent of those polled.

Obama’s proposal for emergency funding, in comparison, was favored by 32 percent and opposed by 38 percent.

Santiago Moncada, a 65-year-old Austin resident who is retired from a state human resources job, said he had considered both proposals and ultimately believes the children need to be deported.

“My heart goes out to them,” said Moncada, a political independent originally from the border city of Eagle Pass. “It needs to be done only because we need to send a message saying our borders are closed. You need to apply for citizenship. You need to apply to come to the United States. You can’t just cross the border illegally.

“My problem is, ‘Who’s going to take care of them?’” Moncada said. “There comes a time when we have to say enough is enough.”

Moncada, however, does support creating a pathway to citizenship for many of the 11 million immigrants who already entered the country illegally. He said many are contributing and should be given a way to become citizens.

A majority of Americans still support such a path to citizenship, though that has slipped to 51 percent from 55 percent in May. Strong opposition to that proposal grew to 25 percent in the new poll from 19 percent in May.

Patricia Thompson’s life has intersected in myriad ways with immigration over the years. She was living in South Florida when thousands of Cubans crossed the Florida Straits fleeing communism. Her son helped build part of the border fence near San Diego with the National Guard. And as an assistant professor of nursing and a college student adviser for four decades, she counseled many immigrant students.

In some cases, those students had been brought to the U.S. illegally as children by their parents, said Thompson, 76, who recently relocated to Florence, Alabama, from Little Rock, Arkansas.

“Those kids certainly deserve an immigration chance,” Thompson said, adding that that issue needs to be resolved before the country moves on to another. For the unaccompanied children crossing the border more recently, Thompson said they should be sent back.

“We’ve got to stop this,” said Thompson, who identified herself as a Republican, but said she thought highly of some of Democratic governors in Arkansas. “We can’t take care of the whole world.”

The poll found that most people — 53 percent — believe the U.S. does not have a moral obligation to offer asylum to people fleeing violence or political persecution. And 52 percent say the children entering the U.S. illegally who say they are fleeing gang violence in Central America should not be treated as refugees.

Eric Svien, 57, a political independent who said he leans conservative, works on the investment side of a bank near Minneapolis, Minnesota. Immigration is not his biggest concern. It ranks somewhere behind reform of the tax code, which he said should be the priority. He said the idea of a moral obligation is a “slippery slope.”

“I think we’ve probably been too open in that regard. I think at this point in time when your country’s resources get strained to the point or you just can’t be the caretaker of the world and you’ve got to draw the line somewhere,” he said. “Where that line gets drawn I hesitate to say … That might be one spot where we have to say enough is enough.”

The AP-GfK Poll was conducted July 24-28, 2014 using KnowledgePanel, GfK’s probability-based online panel designed to be representative of the U.S. population. It involved online interviews with 1,044 adults, and has a margin of sampling error of plus or minus 3.4 percentage points for all respondents.

Respondents were first selected randomly using phone or mail survey methods, and were later interviewed online. People selected for KnowledgePanel who didn’t otherwise have access to the Internet were provided with the ability to access the Internet at no cost to them.